Resolution for 2D art?

Hello Unity forums!
I’m making the first steps towards a 2D sidescroller. I’m using a vector art style for a few reasons, partly because I love using Illustrator and I also love that kind of art.
Anyway, I’m not sure how big the texture files have to be for them to not be pixelated, if I understand correctly, as long as the resolution of a texture is 1:1 to the screen or lower, the texture won’t be pixelated, right?
I’ve started some art on a 2560x1440 artboard with plans to cut most of it up like a spritesheet. This way I can use the artboard as a reference to a high resolution screen, and can scale it down from there for smaller resolutions.
Is this even close to the correct way to do it?
Here is the only example I have: Imgur: The magic of the Internet
Its the player character, dimensions 435x639. Is that too large or am I worrying too much about texture size? (This is a PC game after all)

Also, one more question, might as well ask now: For a 2D background image that goes across the entire level, would it be appropriate to make one file that is very wide, or should I use a bunch of smaller textures?

Thanks, I appreciate any help. Sorry for rambling.
-Zac

Hey mate I asked a similar question a while ago in my thread, some of the answers and conclusions I came to may help :slight_smile: